Skip to main content

Spatial Solitons in Quadratic Nonlinear Media

  • Chapter
Beam Shaping and Control with Nonlinear Optics

Part of the book series: NATO Science Series: B: ((NSSB,volume 369))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).

    Article  Google Scholar 

  2. P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1964).

    Google Scholar 

  3. V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

    MathSciNet  Google Scholar 

  4. A. Hasegawa and F. Tappert, Appl. Phys. Lett. 23, 142 (1973).

    Google Scholar 

  5. L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).

    Article  Google Scholar 

  6. A. Barthelemy, S. Maneuf, and C. Froehly, Opt. Commun. 55, 201 (1985).

    Article  Google Scholar 

  7. J. S. Aitchison, A. M. Weiner, Y. Silberberg, M. K. Oliver, J. L. Jackel, D. E. Leaird, E. M. Vogel, and P. W. E. Smith, Opt. Lett. 15, 471 (1990).

    Google Scholar 

  8. Y. Silberberg, in Anisotropic and Nonlinear Optical Waveguides, C. G. Someda and G. Stegeman eds., chapter 5, pp. 143–157 (Elsevier, Amsterdam, 1992).

    Google Scholar 

  9. A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Clarendon, 1995).

    Google Scholar 

  10. N. N. Akhmediev and A. Ankiewicz, Solitons (Chapman and Hall, London, 1997).

    Google Scholar 

  11. M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992). See Moti Segev’s lectures for a comprehensive review.

    Article  Google Scholar 

  12. Yu. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976).

    Google Scholar 

  13. L. A. Ostrovskii, JETP Lett. 5, 272 (1967).

    Google Scholar 

  14. C. Flytzanis and N. Bloembergen, Prog. Quantum Electron. 4, 271 (1976).

    Article  Google Scholar 

  15. G. I. Stegeman, M. Sheik-Bahae, E. VanStryland, and G. Assanto, Opt. Lett. 18, 13 (1993).

    Google Scholar 

  16. W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).

    Article  Google Scholar 

  17. R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).

    Article  Google Scholar 

  18. R. A. Fuerst, D.-M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).

    Article  Google Scholar 

  19. C. R. Menyuk, R. Schiek, and L. Torner, J. Opt. Soc. Am. B 11, 2434 (1994).

    Google Scholar 

  20. Q. Guo, Quantum Opt. 5, 133 (1993).

    Article  Google Scholar 

  21. R. Schiek, J. Opt. Soc. Am. B 10, 1848 (1993).

    Google Scholar 

  22. A. G. Kalocsai and J. W. Haus, Phys. Rev. A 49, 574 (1994).

    Article  Google Scholar 

  23. I. Ledoux, C. Lepers, A. Perigaud, J. Badan, and J. Zyss, Opt. Commun. 80, 149 (1990).

    Article  Google Scholar 

  24. C. Bosshard, G. Knöpfle, P. Prêtre, S. Follonier, C. Serbutoviez, and P. Günter, Opt. Eng. 34, 1951 (1995).

    Google Scholar 

  25. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. QE-28, 2631 (1992).

    Google Scholar 

  26. M. Houe and P. D. Townsend, J. Phys. D: Appl. Phys. 28, 1747 (1995).

    Article  Google Scholar 

  27. L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, J. Opt. Soc. Am. B 12, 2102 (1995).

    Google Scholar 

  28. E. A. Kuznetsov, A. M. Rubenchik, and V. E. Zakharov, Phys. Rep. 142, 103 (1986).

    Article  MathSciNet  Google Scholar 

  29. K. Hayata and M. Koshiba, Phys. Rev. Lett. 71, 3275 (1993).

    Article  Google Scholar 

  30. M. J. Werner and P. D. Drummond, J. Opt. Soc. Am. B 10, 2390 (1993); Opt. Lett. 19, 613 (1994).

    Google Scholar 

  31. M. A. Karpierz and M. Sypek, Opt. Commun. 110, 75 (1994).

    Article  Google Scholar 

  32. A. V. Buryak and Y. S. Kivshar, Opt. Lett. 19, 1612 (1994); Phys. Lett. A 197, 407 (1995).

    Google Scholar 

  33. L. Torner, Opt. Commun. 114, 136 (1995).

    Article  Google Scholar 

  34. A. V. Buryak, Y. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 1670 (1995).

    Article  Google Scholar 

  35. L. Torner, D. Mihalache, D. Mazilu, E. M. Wright, W. E. Torruellas, and G. I. Stegeman, Opt. Commun. 121, 149 (1995).

    Article  Google Scholar 

  36. A. A. Kanashov and A. M. Rubenchik, Physica D 4, 122 (1981).

    Article  Google Scholar 

  37. S. Trillo and P. Ferro, Opt. Lett. 20, 438 (1995); Phys. Rev. E 51, 4994 (1995).

    Google Scholar 

  38. D. E. Pelinovsky, A. V. Buryak, and Y. S. Kivshar, Phys. Rev. Lett. 75, 591 (1995).

    Article  MathSciNet  Google Scholar 

  39. S. K. Turitsyn, JETP Lett. 61, 469 (1995).

    Google Scholar 

  40. A. D. Boardman, K. Xie, and A. Sangarpaul, Phys. Rev. A 52, 4099 (1995).

    Article  Google Scholar 

  41. L. Berge, V. K. Mezentsev, J. J. Rasmussen, and J. Wyller, Phys. Rev. A 52, 28 (1995).

    Google Scholar 

  42. L. Torner, D. Mihalache, D. Mazilu, and N. N. Akhmediev, Opt. Lett. 20, 2183 (1995).

    Google Scholar 

  43. M. G. Vakhitov and A. A. Kolokolov, Sov. Radiophys. Quantum Electron. 16, 783 (1973).

    Google Scholar 

  44. H. Whitney, Ann. Math. 62, 374 (1954). Other applications can be found in the books about Catastrophe Theory. See also F. Kusmartsev, Phys. Rep. 183, 1 (1989).

    MathSciNet  Google Scholar 

  45. V. V. Steblina, Y. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).

    Article  Google Scholar 

  46. L. Torner, C. R. Menyuk, and G. I. Stegeman, Opt. Lett. 19, 1615 (1994); J. Opt. Soc. Am. B 12, 889 (1995).

    Google Scholar 

  47. L. Torner, C. R. Menyuk, W. E. Torruellas, and G. I. Stegeman, Opt. Lett. 20, 13 (1995); L. Torner and E. M. Wright, J. Opt. Soc. Am. B 13, 864 (1996).

    Google Scholar 

  48. L. Torner and G. I. Stegeman, “Soliton evolution in quasi-phase-matched second-harmonic generation,” J. Opt. Soc. Am. B.

    Google Scholar 

  49. C. B. Clausen, O. Bang, and Y. S. Kivshar, Phys. Rev. Lett. 78, 4749 (1997).

    Article  Google Scholar 

  50. C. B. Clausen, O. Bang, Y. S. Kivshar, and P. L. Christiansen, Opt. Lett. 22, 271 (1997).

    Google Scholar 

  51. L. Torner, W. E. Torruellas, G. I. Stegeman, and C. R. Menyuk, Opt. Lett. 20, 1952 (1995).

    Google Scholar 

  52. W. E. Torruellas, Z. Wang, L. Torner, and G. I. Stegeman, Opt. Lett. 20, 1949 (1995).

    Google Scholar 

  53. W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1449 (1996).

    Article  Google Scholar 

  54. L. Torner, J. P. Torres, and C. R. Menyuk, Opt. Lett. 21, 462 (1996).

    Google Scholar 

  55. G. Leo, G. Assanto, and W. E. Torruellas, Opt. Commun. 134, 223 (1997).

    Article  Google Scholar 

  56. A. D. Capobianco, B. Costantini, C. De Angelis, A. Laureti-Palma, and G. F. Nalesso, IEEE Photonics Technol. Lett. 9, 602 (1997).

    Article  Google Scholar 

  57. L. Torner, D. Mazilu, and D. Mihalache, Phys. Rev. Lett. 77, 2455 (1996).

    Article  Google Scholar 

  58. D. Mihalache, D. Mazilu, L.-C. Crasovan, and L. Torner, Opt. Commun. 137, 113 (1997).

    Article  Google Scholar 

  59. C. Etrich, U. Peschel, F. Lederer, and B. A. Malomed, Phys. Rev. E 55, 6155 (1997).

    Article  Google Scholar 

  60. L. Torner, D. Mihalache, D. Mazilu, M. C. Santos, and N. N. Akhmediev, “Spatial walking solitons in quadratic nonlinear crystals,” J. Opt. Soc. Am. B.

    Google Scholar 

  61. J. F. Nye and M. V. Berry, Proc. R. Soc. London A 336, 165 (1974).

    MathSciNet  Google Scholar 

  62. See, e.g., G. Indebetouw, J. Mod. Opt. 40, 73 (1993).

    Google Scholar 

  63. V. I. Kruglov and R. A. Vlasov, Phys. Lett. A 111, 401 (1985).

    Article  Google Scholar 

  64. I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).

    Article  Google Scholar 

  65. N. N. Rosanov, in Progress in Optics XXXV, E. Wolf ed. (Elsevier, Amsterdam, 1996).

    Google Scholar 

  66. G. A. Swartzlander and C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).

    Article  Google Scholar 

  67. V. Tikhonenko, J. Christou, and B. Luther-Davies, J. Opt. Soc. Am. B 12, 2046 (1995).

    Google Scholar 

  68. Y. S. Kivshar and B. Luther-Davies, Phys. Rep. (1997).

    Google Scholar 

  69. A. V. Mamaev, M. Saffman, and A. A. Zozulya, Phys. Rev. Lett. 78, 2108 (1997).

    Article  Google Scholar 

  70. Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, Phys. Rev. Lett. 78, 2948 (1997).

    Google Scholar 

  71. L. Torner and D. V. Petrov, Electron. Lett. 33, 608 (1997).

    Article  Google Scholar 

  72. J. P. Torres, J.-M. Soto-Crespo, L. Torner, and D. V. Petrov, “Solitary wave vortices in quadratic nonlinear media”, J. Opt. Soc. Am. B.

    Google Scholar 

  73. J. P. Torres, J.-M. Soto-Crespo, L. Torner, and D. V. Petrov, “Solitary wave vortices in Type II second-harmonic generation”, Opt. Commun.

    Google Scholar 

  74. J. M. Soto-Crespo, D. R. Heatley, E. M. Wright, and N. N. Akhmediev, Phys. Rev. A 44, 636 (1991).

    Article  Google Scholar 

  75. N. N. Akhmediev, V. I. Korneev, and Yu. V. Kuz’menko, Sov. Phys. JETP 61, 62 (1985).

    Google Scholar 

  76. L. Torner and D. V. Petrov, J. Opt. Soc. Am. B 14, 2017 (1997).

    Google Scholar 

  77. J. C. Eilbeck, P. S. Lomdahl, and A. C. Scott, Physica D 16, 318 (1985).

    Article  MathSciNet  Google Scholar 

  78. M. Peyrard and M. D. Kruskal, Physica D 14, 88 (1984).

    Article  MathSciNet  Google Scholar 

  79. A. S. Davydov, Solitons in Molecular Systems (Reidel, Dordrecht, 1985).

    Google Scholar 

  80. A. C. Scott, Phys. Rep. 217, 1 (1992).

    Article  Google Scholar 

  81. D. K. Campbell and M. Peyrard, in Chaos, D. K. Campbell ed., (AIP, New York, 1990).

    Google Scholar 

  82. A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 55, 1172 (1996).

    Google Scholar 

  83. G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).

    Article  Google Scholar 

  84. A. V. Buryak, Y. S. Kivshar, and S. Trillo, Phys. Rev. Lett. 77, 5210 (1996); A. V. Buryak and Y. S. Kivshar, Phys. Rev. Lett. 78, 3286 (1997).

    Article  Google Scholar 

  85. U. Peschel, C. Etrich, F. Lederer, and B. A. Malomed, Phys. Rev. E 55, 7704 (1997).

    Google Scholar 

  86. D. Mihalache, D. Mazilu, L.-C. Crasovan, and L. Torner, “Walking solitons in Type II second-harmonic generation,” Phys. Rev. E (1997).

    Google Scholar 

  87. K. Hayata and M. Koshiba, Phys. Rev. A 50, 675 (1994).

    Article  Google Scholar 

  88. A. V. Buryak and Y. S. Kivshar, Opt. Lett. 20, 1080 (1995).

    Google Scholar 

  89. A. V. Buryak and Y. S. Kivshar, Phys. Rev. A 51, 41 (1995).

    Article  Google Scholar 

  90. R. Schiek, Int. J. Electron. Commun. 51, 77 (1997).

    Google Scholar 

  91. T. Peschel, U. Peschel, F. Lederer, and B. A. Malomed, Phys. Rev. E 55, 4730 (1997).

    Google Scholar 

  92. C. Conti, S. Trillo, and G. Assanto, Phys. Rev. Lett. 78, 2341 (1997).

    Article  Google Scholar 

  93. H. He and P. Drummond, Phy. Rev. Lett. 78, 4311 (1997).

    Google Scholar 

  94. S. Trillo, Opt. Lett. 21, 1111 (1996).

    Google Scholar 

  95. B. A. Malomed, P. Drummond, H. He, D. Anderson, and M. Lisak, “Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity,” Phys. Rev. E.

    Google Scholar 

  96. D. Mihalache, F. Lederer, D. Mazilu, and L.-C. Crasovan, Opt. Eng. 35, 1616 (1996).

    Google Scholar 

  97. H. He, M. J. Werner, and P. D. Drummond, Phys. Rev. E 54, 896 (1996).

    Google Scholar 

  98. A. V. Buryak, Phys. Rev. E 52, 1156 (1995).

    Article  Google Scholar 

  99. M. Haelterman, S. Trillo, and P. Ferro, Opt. Lett. 22, 84 (1997).

    Google Scholar 

  100. D.-M. Baboiu, G. I. Stegeman, and L. Torner, Opt. Lett. 20, 2282 (1995).

    Google Scholar 

  101. C. Etrich, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, 3444 (1995).

    Article  Google Scholar 

  102. C. B. Clausen, P. L. Christiansen, and L. Torner, Opt. Commun. 136, 185 (1997).

    Google Scholar 

  103. G. Leo, G. Assanto, and W. E. Torruellas, Opt. Lett. 22, 7 (1997).

    Google Scholar 

  104. S. Trillo, A. V. Buryak, and Y. S. Kivshar, Opt. Commun. 122, 200 (1996).

    Article  Google Scholar 

  105. A. V. Buryak, Y. S. Kivshar, and S. Trillo, Opt. Lett. 20, 1961 (1995).

    Google Scholar 

  106. M. A. Karpierz, Opt. Lett. 20, 1677 (1995).

    Google Scholar 

  107. K. Hayata and M. Koshiba, J. Opt. Soc. Am. B 12, 2288 (1995).

    Google Scholar 

  108. O. Bang, J. Opt. Soc. Am. B 14, 51 (1997).

    Google Scholar 

  109. L. Berge, O. Bang, J. J. Rasmussen, and V. K. Mezsentsev, Phys. Rev. 55, 3555 (1997).

    MathSciNet  Google Scholar 

  110. A. D. Boardman and K. Xie, Phys. Rev. E 55, 1899 (1997).

    Article  Google Scholar 

  111. S. Trillo and M. Haelterman, Opt. Lett. 21, 1114 (1996).

    Google Scholar 

  112. H. He, P. D. Drummond, and B. A. Malomed, Opt. Commun. 123, 394 (1996).

    Article  Google Scholar 

  113. A. De Rossi, S. Trillo, A. V. Buryak, and Y. S. Kivshar, Opt. Lett. 22, 868 (1997).

    Google Scholar 

  114. R. Mollame, S. Trillo, and G. Assanto, Opt. Lett. 21, 1969 (1996).

    Google Scholar 

  115. W. C. K. Mak, B. A. Malomed, and P. L. Chu, Phys. Rev. E 55, 6134 (1997).

    Article  Google Scholar 

  116. P. Algin and G. I. Stegeman, Appl. Phys. Lett. 69, 3996 (1996).

    Google Scholar 

  117. R. A. Fuerst, B. L. Lawrence, W. E. Torruellas, and G. I Stegeman, Opt. Lett. 22, 19 (1997).

    Google Scholar 

  118. D. J. Kaup, A. Reiman, and A. Bers, Rev. Mod. Phys. 51, 275 (1979).

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Kluwer Academic / Plenum Publishers

About this chapter

Cite this chapter

Torner, L. (2002). Spatial Solitons in Quadratic Nonlinear Media. In: Kajzar, F., Reinisch, R. (eds) Beam Shaping and Control with Nonlinear Optics. NATO Science Series: B:, vol 369. Springer, Boston, MA. https://doi.org/10.1007/0-306-47079-9_8

Download citation

  • DOI: https://doi.org/10.1007/0-306-47079-9_8

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-306-45902-3

  • Online ISBN: 978-0-306-47079-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics